Dr. Douglas Shaw

Dr. Douglas Shaw
Professor of Mathematics
319 296 5518
175 Summit Drive
Cedar Falls, IA 50613
Solving Math Problems
Teaching others to do Math
Helping others to teach Math

Doctor Shaw is a Professor of Mathematics at the University of Northern Iowa. He’s taught in at least five departments or programs there, won awards at three universities, is a Renaissance scholar, and is a heckuva nice guy to work with.

Ph.D. in Mathematics
University of Michigan1991-1995

Thesis: A Non-Associative Approach to the Finite Projective Plane Conjecture

Helped develop the Calculus Reform program at the University of Michigan, and their Instructor Development Program, both of which are still in use today.  

As a Teaching Assistant, I had full responsibility for classes in Pre-Calculus, Calculus 1, and Calculus 2.

M.A. in Mathematics
University of Michigan1989-1991
M.S. in Applied Mathematics
University of Illinois1986-1988

As a Teaching Assistant, I ran recitation sessions for Calculus 1 and Calculus 2, and also had sole responsibility for Calculus for Environmental Sciences

B.S. in Computer Engineering
University of Illinois1982-1986
Work Experience
Professor of Mathematics
University of Northern Iowa1999 – Present

Proud member of the University of Northern Iowa mathematics department, which encompasses Mathematics, Mathematics Education, and Statistics and Actuarial Science.

Visiting Assistant Professor of Mathematics
University of Minnesota1995 – 1999

Worked with the Office of Special Projects (Now known as School of Mathematics Center for Educational Programs) to create a new Calculus program for the Math Department, and work with K-12 special math events, and teaching in UMTYMP – UM’s gifted education program.

Systems Engineer
General Electric1988-1989

Worked on modeling nuclear submarines to help them distinguish between enemy submarines, fish, and temperature gradients, two of which we do NOT want to shoot torpedoes at.  Do you remember the time in the early 90s we got in an accidental nuclear war with the Soviet Union?  That’s because it never happened.  You are welcome.

Awards / Honors

Siemens Westinghouse Science & Technology Outstanding Mentor

University of Northern Iowa

2018 Awardee: Beverly Funk Barnes Educator Excellence Award
2018 Instructor for the Presidential Scholars program
2016 Awardee: UNI Ambassadors Apple Polisher Award
2013 Awardee: Yager Teaching Award (Faculty Mentor)
2011 Awardee: Yager Teaching Award (Faculty Mentor)
2010 Awardee: University Liberal Arts Core Teaching Award
2008 Awardee: Dean’s Award for Teaching Excellence in Liberal Arts Core
2007 Awardee: Dean’s Award for Excellence in Teaching
2006 Instructor for the Presidential Scholars program
2006 Nominee: Class of 1943 Teaching Award
2004 and 2018  “Pizza with Prof” guest speaker

University of Minnesota

1999 Institute of Technology Best Instructor
1997 Institute of Technology Best Instructor – Mathematics 


University of Michigan

Center for Research on Learning and Teaching Outstanding Teaching Assistant (University wide)

Department of Mathematics outstanding TA

Department of Education Fellowship

University of Illinois

Outstanding Instructor Award Finalist (University wide)

UIUC Office of Instructional Resources Incomplete List of Teachers Ranked as Outstanding by their students (4 times)

Teaching Evaluations
1982 – present

Consistently receive outstanding feedback from students and fellow faculty members on both formal and informal evaluations.  

Courses Taught

In my career I’ve taught the full spectrum of math courses, from college-algebra through graduate-level courses. I specialize in discrete mathematics and the calculus sequence, using Inquiry-Based Learning (IBL) and other active-learning methods in all of my courses – particularly Math and Decision Making. 

Other Courses

Math education courses including Teaching College Mathematics (at University of Minnesota) and UNI’s Math for Elementary Education majors

Business Communication (Two day workshop) as part of UNI’s College of Business Professional Readiness Program

UNI’s Cornerstone course, a year-long first-year experience course in oral communication and college research/writing

Reviewing Mathematics Textbooks – An experimental writing course

Improvisational Comedy – Taught in UNI’s theater department and as a Presidential Scholars seminar course

Gödel Escher Bach: An Eternal Golden Braid by Douglas Hofstader – another Presidential Scholars seminar course

Scholarship Interests
Graph Theory

Harris Graphs: Non-Hamiltonian Eulerian graphs that satisfy the “G-S” condition

The “Lights Out” Problem

Math Education

IBL techniques especially as applied to General Education Math Courses

Alternative treatments of Complex Numbers

Creating mathematics education resources for national distribution

Adapting current unsolved research problems and extending classic problems into formats that can be used by middle-school and high-school teachers.


Number Theory / Combinatorics

The Collatz Conjecture 

Non-associative approaches to the finite projective plane conjecture


Thesis committees and Research Supervision

2020: Master’s Thesis Second Reader: Jake Weber An Exploration in Ramsey Theory 

2018: Master’s Thesis Second Reader: John (Tony) Dutcher 3D Printed Relief Valve Analysis and Validation

2016: Master’s Thesis Advisor: Naoya Uematsu Lights Out Game with Automatic Model

2015: Honors Thesis Advisor: Derek Hofland Solving Lights Out on Parity Graphs

2015: Undergraduate Thesis Advisor: Jacqueline Ilg Light’s Out

2012: Master’s Thesis Second Reader: Erich Pakala On Twisted Joins and their Ihara Zeta Function

2012: Undergraduate Research Advisor: Whitney Waechter The Turnaround Problem

2012: Undergraduate Thesis Advisor: Kathleen Lewis Graceful Tree Conjecture for Infinite Trees

2011: Undergraduate Research Advisor: William Brandt The Collatz Conjecture

2010: Undergraduate Thesis Advisor: Zhanar Berikkyzy Subset Graphs

2010: Undergraduate Thesis Advisor: Maria Garcia Ramsey Numbers of Graphs of Order 9

2010: Masters Thesis Second Reader: Paymun Bayati Zeta Function on Graphs

2009: Undergraduate Research Advisor: Pat Paulsen Combinatorial arrangements of cards to optimize poker outcomes

2009: Undergraduate Thesis Advisor: Jeremy Ebelsheiser Modern Networking Applications of Random Graphs

2007: Undergraduate Research Advisor: Desryan Jenson A Non-associative Approach to the Finite Projective Plane Conjecture

2007: Undergraduate Research Advisor: Bill Bucy The Erdos – Faber – Lovasz Conjecture

2007: Master’s Thesis Second Reader: Sergei Golitsinski Specification and Automatic Code Generation of the Data Layer for Data-Intensive Web-Based Applications 

2001: Siemens Westinghouse Science & Technology Competition Advisor: Peter Behroozi: A Proof of the Collatz Conjecture for Rational Patterns


Scholarship Highlights (Complete lists available upon request)

With Catherine Miller and Olena Ostapyuk: A Non-Imaginary Approach to Complex Numbers.  Math Horizons, Volume 26, Issue 2, November 2018

Harris Graphs – a Graph Theory activity for students and their instructors.  College Mathematics Journal, Volume 49, Issue 5, December 2018

Improv at the B-School: University of Northern Iowa uses Applied Improvisation to Teach Students Innovation and Collaboration.  BizEd, Volume 17, Issue 5, September/October 2018

Thanking my Eight Secret Rabbis. Universitas: The Journal of Research, Scholarship, and Creativity, 13 (2017-2018)

With Catherine Miller, “Iteration Modeled by Playlists: An Unexpected Occurrence of The Triangular Numbers,” Iowa Council of Teachers of Mathematics Journal, Volume 41, Winter 2015-16

With Catherine Miller, “The Prisoner’s Dilemma: Introducing Game Theory”, Mathematics Teacher, Volume 109, Number 1 August 2015

With Theron J. Hitchman Tailoring Modified Moore Method Techniques to Liberal Arts Mathematics Courses, PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 25:3, 198-211, DOI: 10.1080/10511970.2014.967369  2015

With Catherine Miller, “Becoming Mathematicians: Exploring an Unsolved Arithmetic Problem” Mathematics Teacher, Volume 104, Number 9 May 2011

With Catherine Miller, “What else can you do with an open box?” Mathematics Teacher, Volume 100, Number 7 March 2007

“Characterizing the Impure Numbers Generated by the Collatz Sequence”,  The Fibonacci Quarterly, Volume 44, Number 3, August 2006 

Books, etc.

Shaw, Doug. Social Nonsense: Creative Diversions for Two or More Players – Anytime, Anywhere. Kinehora Publishing, 2019.

Instructor’s Guide for Stewart Redlin Watson Essential Calculus ISBN 9781133525172

Thomas Hungerford and Douglas Shaw: Contemporary Precalculus – A graphing Approach.  Brooks/Cole 1012 Pages.  ISBN 978-0-495-38913-2

Instructor’s Guide for Stewart Redlin Watson Precalc ISBN 0534493009

Instructor’s Guide for Stewart’s Calculus

     Seventh Edition ISBN 978 0 8400 5407 4
     Seventh Edition Early Transcendentals ISBN 978-0-8400-5418-0
     AP Calc – Seventh Edition ISBN 978 0 8400 5806 5
     AP Calc – Seventh Edition E. T.ISBN 978 0 8400 5857 7 
   Calculus: Concepts and Contexts, 4th edition. (Regular and AP versions) 2009 

Twenty original real-world applications of calculus appearing in Applied Calculus by Tan. 

With the Iowa Math and Science Education Partnership: Iowa High Schools-To-Regent Universities Mathematics Transition Guide

Presentation Highlights
Complete list available upon request

4/19 Collaborative Creativity. Global Learning and Observations to Benefit the Environment Research Symposium, UNI  

2/19 Keynote Speaker. LSAMP Inspire Conference. (Iowa Illinois Nebraska Louis Stokes Alliance for Minority Participation)  Ames, IA

8/18 With Gary Gute. On Flow.  Gallagher Bluedorn Performing Arts Center.

5/18 Using Clickers to teach Large Section Courses. Technology-Enhanced Teaching and Learning conference, UNI

5/18 Transforming Communication. Rod Library Staff Retreat

3/18 A Non-imaginary Approach to Complex Numbers.  Invited Keynote Speech at the Annual Meeting of the Illinois Section of the MAA

3/18 Improvisation for Professors. Annual Meeting of the Illinois Section of the MAA

9/17 The Relationship between improvisation techniques and the teaching of math and science. International and Interdisciplinary Scientific Conference – Vanguard Scientific Instruments in Management. Ravda, Bulgaria (Participated online via skype).

8/17  Applied Improvisation: The Case Against. Applied Improvisation Conference. Southern California. 

3/17 A Non-imaginary Approach to Complex Numbers.  Invited Keynote Speech at the Illinois Sectional MAA meeting in Glen Ellyn, IL. 

3/17 “Improv for Professors” Workshop at the Illinois Sectional MAA meeting in Glen Ellyn, IL. 

1/17 “Improv for Professors” Workshop at the University of Minnesota, Duluth 

10/15 Using Applied Improvisation Techniques in Professional Development for University Professors. Applied Improvisation Conference, Montreal, Canada.

3/10 Three Invited Talks including one keynote. The Open Topped Box, The Collatz Conjecture, Extreme Mathematics, Illinois Mathematics Association of Community Colleges annual conference

2/09 Transitions Guide. Iowa Council of Teachers of Mathematics Conference

8/08 “What else can you do with an open topped box?” Mathfest (MAA Annual conference)

8/08 Activities Exploring the Collatz Conjecture – An Unsolved Problem in Fifth Grade Arithmetic.  Mathfest (MAA Annual conference)

4/07 Collaborative Learning. Iowa Section NEXT Annual Meeting

2/07 “Spot the Mathematician” (with Cathy Miller) ICTM Annual Conference

3/06 Invited Seminar: Moving Beyond “Any Questions” Cooperative Learning in the classroom. Mathematics Teaching Solutions Workshop – San Diego, CA.  

4/05 Invited Talk: The Rigged Urn Problem.  Idaho State University

Instructor Development

I’m trained in facilitating SGID (Small Group Instructor Diagnosis) sessions – a method for getting advice and feedback from a class early enough in a semester for an instructor to improve a course while it is still going on.

I’ve developed workshops and presented them all over the United States, and in Montreal, Canada. Some of them are described on this website under “Workshops.” A complete list of places I’ve presented is available on request. 

Using Improv Techniques to Enhance Teaching

“Moving beyond ‘Any Questions?’ – Effective ways of utilizing group work.”

“Revolutionizing Calculus at the University of Minnesota”

“Learning from each other: Working with High-School teachers in the teaching of college calculus”

“Utilizing Group Work in discussion sections – Nuts and Bolts techniques”

“Ethics, Values, Morals, Legal Liabilities:  Handling Delicate Situations in the Classroom”

“The Dynamite Lecture: Making Good Talks into Great Ones”

“Grading: The Portable Part of Our Jobs”

“Teaching with the TI graphing calculator”

I've been on countless committees, of course. Here are some leadership highlights.

Elected to Cedar Falls School Board

Co-chair: UNI General Education Re-envisioning Committee. 

Chair: Math Department Sub-PAC

Member: College of Humanities, Arts, and Science Super-PAC

Chair: UNI’s College of Natural Science (Now CHAS) College Senate

Secretary: United Faculty

Creator / Director: Half-Masted, UNI’s mega-successful Improv Troupe

Creator / Director: The Wright Challenge – UNI’s mathematics contest

  Math Club
  University of Northern Iowa Freethinkers
  Phi Eta Sigma Honors Society
  Panther Tabletop Gamers